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- Jun 20, 2014

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Let $A$ be a commutative ring with unity. Prove that a polynomial $p(x) = a_0 + a_1 x + \cdots + a_n x^n$ over $A$ is a unit in $A[x]$ if and only if $a_0$ is an $A$-unit and $a_1,\ldots, a_n$ are nilpotent in $A$.

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